If a stock with Geometric Brownian Motion dynamics like the Black & Scholes model: dSt St = dt + dWt and there is also a money-market account with dynamics dBt Bt = rdt, where r is a positive known constant.

Couple of questions in my mind:

What is the (i.e., the sensitivity of the price with respect to the underlying asset price) and (i.e., the sensitivity of the with respect to the underlying asset price) of a straddle portfolio (i.e., buying a European call and a European put together with same strike price K and maturity T), as a function of the delta and gamma of the corresponding call option, C and C?

Under which condition is the straddle delta-neutral???? Also why do investors actually prefer low gamma or even gamma-neutral portfolios??

Like what is the sign of (i.e., the sensitivity of the price with respect to ) of this straddle and what is right before the straddle expires?